Partitioning Boolean lattices into chains of subsets

We prove that the Boolean lattice of all subsets of an n-set can be partitioned into chains of size four if and only if n9.Research supported in part by N.S.F. grant DMS-8401281.Research supported in part by N.S.F. grant DMS-8406451.     

Two-photon absorption and energy band structure of orthorhombic Hg2Cl2 crystals

Dependence of two-photon absorption (TPA) rate on the state of polarization of a laser beam is investigated in the low-temperature orthorhombic modification of Hg₂Cl₂ crystals. Theoretical calculations of the dependence of TPA rate on the direction of polarization vector of the beam are performed for centrosymmetric points, Y, Z, T, R andS of the Brillouin zone. The domain structure of real crystals is taken into consideration and it is shown that periodicity of the polarization dependence may indicate whether TPA is due to transitions either at, Y, Z, T orR, S points. The polarization dependence of TPA cannot, however, distinguish between points inside these two groups. Comparison of theory with a low-temperature (T 8·5 K) experimental curve of polarization dependence is discussed. It is shown that the experiment can be explained in main features by a model of noninteracting oriented linear dipoles. Further, on the basis of TPA measurements, a simple energy band structure of Hg₂Cl₂ is proposed regarding Hg₂Cl₂ crystal as a linear chain of molecules.The authors express thanks to Dr. . Barta for supplying the Hg₂Cl₂ crystals, Dr. Z. Bryknar for critical comments and Dr. B. Velický for stimulating discussion. We thank also Dr. V. Kohlová for assistance during measurement.     

CO laser stabilization using the optogalvanic Lamb-dip

Frequency stabilization of the CO laser using a CO lamb-dip is achieved in the range from 5.0–6.3 m. The CO saturation signal is obtained from a low-pressure discharge in absorption and is detected using optogalvanic, detection. The frequency stability and reproducibility has been verified to be better than 100 kHz; this is an improvement of more than one order of magnitude compared with locking techniques using CO laser gain profiles.Alexander von Humboldt Awardee from National Bureau of Standards, Boulder, Colorado, USA     

Multiparticle excitations in142Nd

An (α, 2nγ) in-beam study of excited states in 142Nd revealed 27 new levels on top of the 6⁺ isomer. Nanosecond lifetimes were found for two levels. The measured excitation energies were compared with spherical shell-model predictions obtained from suitably truncated model spaces.     

Vibrational modes and infrared absorption of interstitial oxygen in silicon

A quasi-linear Si₂O molecule model (QLMM) is suggested from an analysis of the configuration and the interactions of an isolated oxygen atom with its neighbor silicon atoms. The vibrational modes are assigned and the infrared absorption spectra are calculated in detail with the model. The theoretical results are in reasonably good agreement with reported experimental values. This agreement shows that for the analysis of the vibrational modes of the interstitial oxygen atom in silicon crystals it is not necessary to consider the coupling of the molecule with the rest of the lattice. The interaction of the oxygen atom with its six second-nearest silicon atoms only causes the level separation of the ₂ mode and the formation of the fine structure.     

Toward molecular electronics

A polarized N-O bond behaves as an intramolecular p-n junction. Their rectifying properties have been found in 1,3-dimethylisoxasole, 1-phenylsydnone, and 1-(4-methylphenyl)sydnone molecules based on H¹-NMR data.